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MATERIALS SCIENCE & ENGINEERING

MATERIALS SCIENCE & ENGINEERING. Part of. A Learner’s Guide. AN INTRODUCTORY E-BOOK. Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh.

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MATERIALS SCIENCE & ENGINEERING

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  1. MATERIALS SCIENCE & ENGINEERING Part of A Learner’s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email:anandh@iitk.ac.in, URL:home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm

  2. D Size Factor compounds: (i)Laves phases (ii) Frank-Kasper Phases D(i) Laves Phases • These phases have a formula: AB2 • Laves phases can be regarded as Tetrahedrally Close Packed (TCP)* structures with an ideal ratio of the radii (rA/rB) = (3/2)1/2 ~1.225[or usually rA/rB (1.1, 1.6)] • If rA/rB = 1.225 then a high packing density is achieved with the chemical formula AB2 with a average coordination number of 13.3 • Crystal structures: Hexagonal→ MgZn2 (C15), MgNi2 (C36) FCC→ MgCu2 (C14) • There are more than 1400 members belonging to the ‘Laves family’ • Many ternary and multinary representatives of the Laves phases have been reported with excess of A or B elements. Some ternary Laves phases are known in systems with no corresponding binary Laves phases. • The range of existence of the three phases (C15, C36, C14) in ternary Laves phases is influenced by the e/a ratio * Also called Topologically Close Packed structures?

  3. Laves phases containing transition metals as components have interesting Physical and mechanical properties. Engineering materials based on Laves phases are being developed for: High temperature applications (for use in turbine blade fine precipitates of Laves phases is shown to improve fatigue strength) Hydrogen storage applications (in nickel-metal hydride batteries)

  4. C14 MgZn2 Laves Phase Hexagonal [0001] Zn: Vertex-1, Edge-1, Inside cell-6 → 8 Mg: Inside cell-4 → 4 Mg Zn2 Zn1 Unit cell formula: Mg4Zn8

  5. Constructing the hexagonal laves phase More views MgZn2 Laves Phase Start with a layer of Zn atoms Put Mg atoms in the depressions formed in the layer (above and below) This gives us half the unit cell in ‘c’ direction Add a hexagonal array of Zn atoms in the depressions formed by the Mg atoms (above and below)

  6. MgCu2 Laves Phase C15 Cubic [001] Very frequent structural type Mg: Vertex-1, FC-3, Inside cell-4 → 8 Cu: Inside cell-16 → 16 Cu (16d) Mg (8a) Unit cell formula: Mg8Cu16

  7. MgCu2 Laves Phase More views Successive layers are build on the depressions on the previous layer

  8. MgCu2 Laves Phase More views Tetrahedra of Cu Note: the solid lines in the figures are for visualization of atomic positions etc. (they are not meant to show bonds) Not to scale

  9. D(ii) Frank-Kasper • Have coordination numbers (CN): CN =12, CN = 14, CN = 15, CN = 16

  10. Cubic CN =12 Al12W Frank-Kasper Phase [001] W: Vertex-1, BC-1 → 2 Cu: FC-12, Inside cell-12 → 24 Unit cell formula: Al24W2 Al Motif: 12Al +W (consistent with stoichiometry) Lattice: Body Centred Cubic W

  11. More views Al12W Frank-Kasper Phase • Icosahedral coordination around W atoms • Local icosahedral symmetry is destroyed in the long range packing • Note that icosahedral symmetry is not found in crystals • This phase is closely related to quasicrystals

  12. More views Al12W Frank-Kasper Phase [100] [110] [111]

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